Radar system for determining the muzzle velocity or time of flight of a projectile



y 4, 1965 c. R. CLEMENCE El AL 3,182,313 4 RADAR SYSTEM FOR DETERMININGTHE MUZZLE VELOCITY OR TIME OF FLIGHT OF A PROJECTILE Filed April 1,1953 11 Sheets-Sheet 1 May 4, 1965 c. R. CLEMENCE ETAL RADAR SYSTEM FORDETERMINING THE MUZZLE VELOCI OR TIME OF FLIGHT OF A PROJECTILE llSheets-Sheet 2 Filed April 1, 1963 May 4, 1965 c. R. CLEMENCE ETAL3,182,313

RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCITY 0R TIME OF FLIGHT OF APROJECTILE ll Sheets-Sheet 5 Filed April 1, 1963 Aw% m "u -q di udj NL mv mmfi J F N h May 4, 1965 RADAR SYSTEM FOR DETERMINING THE MUZZLEVELOCI Filed April 1, 1963 OR TIME OF FLIGHT OF A PROJECTILESheets-Sheet 4 ,4M/-/ PM) C) C) W #5 I .2 I 15 7Q- [2 9 4M// ,PM/ #5 #5C) (D r ,0142 [6 PM Q66 #5 1% (D G) M y 1965 c. R. CLEMENCE ETAL3,182,313

RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCITY OR TIME OF FLIGHT OF APROJECTILE Fil April 1 1963 ll SheetsSheet 5 I I Cg }1P M [6 //M// A a?,P/W/ H5 (Md/Q H5 (1 r/a z/a al/wwu May 4, 1965 c. R. CLEMENCE ETAL3,182,313

RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCITY OR TIME OF FLIGHT OF APROJECTILE XWWM MMZ WW May 4, 1965 c. R. CLEMENCE ET AL 3,182,313

QR DETERMINING THE MUZZLE VELOCITY RADAR SYSTEM F OR TIME OF FLIGHT OF APROJECTILE ll Sheets-Sheet 7 Filed April 1, 1963 m m M P T c w w i 7 1/a H a M T f w 7 4 Z 4 g 2 I FILJ M p T 4 W M /H 5 VI 2 {#3 0 1 W M. 4 MJ r k DA.

y 1965 c. R. CLEMENCE ETAL 3,182,313

RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCITY OR TIME OF FLIGHT OF APROJECTILE Fll p l 1, 1963 11 Sheets-Sheet 8 May 4, 1965 c. R. CLEMENCEETAL 3,182,313

RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCITY 0R TIME OF FLIGHT OF APROJECTILE Flled Aprll 1, 1-963 11 Sheets-Sheet 9 May 4, 1965 c. R.CLEMENCE ETAL RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCI 0R TIME OFFLIGHT OF A PROJECTILE l1 Sheets-Sheet 10 Filed April 1, 1965 May 4,1965 RADAR SYSTEM FOR DETERMINING THE MUZZLE VELOCITY OR TIME OF FLIGHTOF A PROJE CTILE l1 SheetsSheet 11 Filed April 1, 1963 T C. R. CLEMENCEETAL United States Patent RADAR SYSTEM FOR DETERMINING THE MUZZLEVELOCITY 0R TIME OF FLIGHT OF A PROJECTELE Charles R. Clemence andWilliam C. Brown, Ottawa,

Gntario, Canada, assignors to National Research Council, Ottawa,Ontario, Canada, a body corporate Filed Apr. 1, 1963, Ser. No. 269,282Claims priority, applicatioii Canada, Nov. 20, 1962,

86 6 Claims. (Cl. 343-7) This invention relates to a radar system andmethod, for use in locating enemy weapons (such as mortars) by obtainingechoes from the projectiles fired by such weapons.

The invention is concerned with a radar system for determining at leasttwo points through which a projectile passes, and including a computerfor determining the point of intersection of the trajectory of theprojectile with the ground from two of such determined points. Whendesired for greater accuracy, the time interval required for passage ofthe projectile between said two points is inserted into the computer.Such a system is of particular utility when the weapon is hidden fromdirect visual or radar observation.

The radar system is equally useful for watching friendly projectilesaimed at the enemy weapon and for determining the points of impact orburst of such friendly projectiles by making the same extrapolation onthe trajectory of a falling projectile as for a rising projectile. Thepoint to be located (usually on the ground) through which suchtrajectory extends (whether for a rising or falling projectile) iscalled the target point. In the general case, the target point is thepoint of intersection of the projectile trajectory with a selected planereferred to as the working plane. The working plane is defined as theone including the line between the radar system and the target point andall horizontal lines perpendicular to said line. The angle of theworking plane will generally be chosen to give a ground location for thetarget point unless tactics otherwise demand.

Such a system is described in W. C. Brown et a1. United States patentapplication Serial No. 269,367, filed April 1, 1963. This applicationdescribes a system the antenna of which provides a narrow beamsubstantially circular in cross section having a width of approximately16 mils (approximately 1, a mil being 360/6400 in both directions. Thesystem causes this narrow beam to scan horizontally throughapproximately 400 mils (22.5") alternately in two planes separated inangle by approximately 40 mils (2.25") at beam centres. This action defines, by the narrow beam locus, two vertically superposed, generallyhorizontal, fan-shaped beams, each scanned 20 times per second,hereinafter referred to as the upper and lower beams.

Echoes (intercepts) received from each of the upper and lower beams whena projectile passes through it, are displayed on a range-azimuth radardisplay in two series (one for each of said beams). The duty of theoperator is to observe or mark the centre points of the leading edges ofthe first and last echoes received in each of the upper and lower beamsand to estimate and mark the mean points between each pair of these twoextreme centre points. The radar screen is provided with an outersurface that can readily be marked by the operator using a suitablestylus. Having marked the mean centre points on the screen, the operatorthen feeds information concerning the positions of these points into acomputer which calculates an extrapolated target point on the Workingplane through which the projectile trajectory passes. The computerdisplays the position of this target point in counters as representingthe position of the weapon. During the course of this operation, theoperator normally also determines AT, the time between the projectilebeing in similar positions in each of the upper and lower beams.

Such similar positions can conveniently be the points of entry of theprojectiles into each of said beams.

The system outlined above was developed especially for observing enemymortar fire, or fire from other high angle weapons. It can similarly beused for watching friendly projectiles and calculating their point ofimpact or burst, but again the prime purpose of the system has beendirected to use with weapons having high angle traject-ories.

it is often of value to military forces to know the nature of the enemyweapon, and this can often be deduced if the muzzle velocity of theprojectile is known. It is an object of the present invention to providea mechanism, for use in conjunction with the radar system aforesaid,that will furnish an estimate of the muzzle velocity of a projectileobserved.

Another function closely related to muzzle velocity is the time offlight of the projectile. Sometimes it is more convenient to know thetime of flight than to know the muzzle velocity, and hence a furtherobject of the invention is to provide a mechanism that will furnish anestimate of the time of flight. Conveniently, a single mechanism will beconstructed to yield either or both functions (muzzle velocity and timeof flight) as required. In practice the utility of the invention islimited to use with comparatively high angle projectiles (such as mortarshells), as the assumptions made for the calculations would beinsuiliciently accurate for projectiles with low angle trajectories.

The objects of the invention are achieved by the provision of a radarsystem comprising (a) Means for emitting two closely verticallysuperposed,

mutually divergent, generally horizontal, effectively continuous upperand lower radar beams,

(b) Means for displaying echoes returned by a projectile travelling in atrajectory intersecting said upper and lower beams and for determiningthe range value (R of one of said intersections measured from the radarsystem,

(c) Means for determining the time interval (AT) between passage of theprojectile through corresponding points of the upper and lower beams,

(d) And mechanism for solving the equation V z Ga t 02% where V is themuzzle velocity of the projectile, t, is the time of flight of theprojectile, and C and C are constants,

(e) And means for inserting the values of R and AT into such mechanismto derive at least one of the quantities V and t One manner of carryingthe invention into practice is illustrated diagrammatically in theaccompanying drawings. The specific system illustrated is provided byway of example only, the broad scope of the invention being limited onlyby the appended claims. In these drawings:

FIGURE 1 is a general perspective view of a radar system according tothe invention in operation,

FIGURE 2 is a first diagram of a typical projectile trajectory,

FIGURE 3 is a further diagram of another projectile trajectory,

FIGURE 4 is a plan view of the diagram of FIGURE 3, also showing theposition of the radar system,

FIGURE 5 is another diagram provided to illustrate the geometry of thecomputations,

FIGURE 6a is a plan view of the area scanned by the radar system,

FIGURE 6b demonstrates the manner of presenting such area of scan(FIGURE 6a) on a radar B-scope during a long range searching sweep,

FIGURE 6c shows a portion of the presentation of FIGURE 6b enlarged asit appears for a short range sweep,

FIGURE 7a is a simplified front view of a portion of the radar controlpanel illustrating diagrammatically the appearance of an echo of aprojectile on the screen,

FIGURE 7b is another View similar to FIGURE 7a, a short time later inoperation,

FIGURE 7c is yet another view similar to FIGURES 7a and 7b at a laterstage,

FIGURE 7d is another similar view at yet a later stage in the radarobservance of a projectile,

FIGURE 7e is a View similar to FIGURES 7a to d showing the marks made bythe operator after the projectile echoes have faded and the manner ofuse of a marker spot,

FIGURE 7 is a view similar to FIGURE 7e at a later stage in operation,

FIGURE 8 is a general overall circuit for the radar system,

FIGURE 9 is a more detailed illustration of the portion of the circuitof FIGURE 8 principally concerned with calculating the range of thetarget point,

FIGURE 10 is a more detailed illustration of the portion of the circuitof FIGURE 8 principally concerned with calculating the elevation of thetarget point and providing certain parameters to the range and azimuthportions,

FIGURE 11 is a more detailed illustration of another portion of thecircuit of FIGURE 8 principally concerned with calculating the azimuthof the target point,

FIGURE 12 is a detailed illustration of the portion of the circuitprovided to display the information in the most conveniently usableform,

FIGURE 13 is a diagram of a projectile trajectory illustrating thegeometry of the problem involved in determining muzzle velocity of timeof flight; and

FIGURE 14 is a diagrammatic representation of mechanism for determiningmuzzle velocity and time of flight I according to the invention.

Overall system (FIGURE 1) FIGURE 1 shows the radar system RD mounted ona vehicle V being used to observe the trajectory T of'a projectile firedby a mortar positioned out of direct visual or radar range behind hillsH. The antenna system of the radar system RD provides a narrow beamsubstantially circular in cross-section having a width of approximately16 mils (approximately 1, a mil being 360/6400) in both directions. Thesystem causes this narrow beam to scan horizontally throughapproximately 400 mils (22.5 alternately in two planes P1 and P2separated in angle by approximately 40 mils (2.25) at beam centres. Thisaction defines, by the narrow beam locus, two vertically superposedfan-shaped beams, each scanned 20 times per second, hereinafter referredto as the upper and lower beams. This effect is achieved by use of aFoster type scanner SC similar to that disclosed in Foster U.S. PatentNo. 2,832,936 issued April 29, 1958, and modified to provide a dualbeamin a manner similar to that de- "scribed in Mobile Radar PinpointsEnemy Mortar Positions, by M. S. I affee et al., Electronics, September18, 1959, page 34 et seq. The scanner SC is placed at the focus of asemi-parabolic cylinder RF which reflects two focused beams. The scannerSC and reflector RF are mounted as an assembly on an antenna platform APon the vehicle V, which platform is maintained horizontal at all times(see United States patent application No. 269,363, filed April 1, 1963).The scanner-reflector assembly can be inclined relative to thishorizontal platform AP to alter the angle of sight of the beams as apair while maintaining constant their angular separation. The limits 4of this adjustment may for practical purposes be set at 212 mils (12)above the horizontal to 106 mils (6) below the horizontal, these anglesbeing between the horizontal and the lower beam plane P The antennaassembly can be rotated to provide complete coverage throughout 6400mils (360) in azimuth.

Mathematics of the computations to be made (FIGURES 2 t0 5) Beforeconsidering the detailed nature of the display which appears on theradar screen as a result of a projectile passing through the upper andlower beams, it is necessary to consider the mathematics of the problem,taking as a first assumption that the echoes received from each beam canbe resolved into a single point on the trajectory T of the projectile,the range and azimuth of which point thus becomes known. The angle ofsight 0 of the lower beam to the horizontal is known by the settingapplied to the scanner-reflector assembly by the operator. In practice,the operator will make this angle of sight as small as he may havingregard to the limitations of the terrain. He will normally aim theantenna so that the lower beam just clears the treetops, or other highpoint, such as the upper outline of the hills H in FIGURE 1. He may beprovided with a telescope aligned with the lower beam to facilitate thissetting.

FIGURE 2 shows two intercept points a and b on trajectory T determinedby the radar system RD at ranges R and R respectively, it being assumedfor simplicity in this first diagram that the trajectory T is directedstraight towards the radar system RD with no change in azimuth betweenpoints a and b. The angle of sight of the lower beam is shown as 0, andthe fixed angle between the two beams is designated a. The anglerepresents the difference between the horizontal plane HP through theradar system RD and the working plane WP which is the plane in whichboth the radar system RD and the target point lie. The target point willbe assumed to be occupied by an enemy mortar for the presentdescription. The mortar is in fact positioned at the point M which isthe extrapolation of the trajectory T from points a and b to the workingplane WP, assuming the trajectory to be substantially parabolic. Point Mwould be the position of the mortar if it were on the horizontal planeHP, and points 1 and f are the corresponding points on the horizontaland the working planes for a straight line extrapolation from points aand b.

It will be appreciated that the angles at which the radar system isworking in practice will be very small compared with the angles actuallyshown in FIGURE 1. It is necessary to exaggerate the size of the anglesin FIGURE 1 in order to have a workable diagram. With this point in mindit will be appreciated that many of the approximations employed in thesubsequent calculations are in fact a good deal closer to being truethan would at first sight appear from FIGURE 1, by reason of the factthat such small angles are encountered in practice.

Consider first the straight line extrapolation back from points a and bto point 1. Since triangle bca is similar to triangle aef ef e a as beThus R 9 ef- ARKAR This function thus represents the correction forstraight line extrapolation, where a constant times 0 and thus varieswith that angle. As above indicated, the working plane WP is provided totake care of the situation occurring when the position of the mortar Mis above or below that of the radar system RD, e.g. at M. An estimatedworking plane is initially assumed by the operator as a roughcalculation from a contour map, since he knows the general location ofthe mortar, and is later corrected as required in a manner to bedescribed below. The operators initial estimate of the working planeangle qb radians does not affect the angle of sight 0 of the radarslower beam; it merely plays a part in the calculations.

Taking the working plane WP into account namely a constant times (H- s).

The mortar range Rm has now been found as R +KAR.

FIGURE 2 assumes that the mortar is firing directly towards the radarsystem RD. FEGURES 3 and have been constructed with a differentassumption, namely that the mortar is firing exactly at right angles tothe line of sight from the radar system RD. Under these conditions thereis a change in azimuth, but no change in range, between the two detectedprojectile intercepts a and 17. A and A (FIGURES 3 and 4) are assumed tobe the azimuth angles in radians from a convenient datum (such as North)of the detected points a and b.

As FIGURE 4 shows ca-( A )R=AA R, where 12:13:12,.

Also

ae-R6 and lJC Roc where 0 and a have the meanings already ascribed tothem.

Consequently efPeKAA R where as before.

The mortar azimuth Am has now been found as A -l-KAA.

it the mortar is not firing directly towards the radar system RD or on aline perpendicular to it, but at some angle in between, the samediagrams will apply for the components, and in the general case therewill be both AR and AA factors for each trajectory. To visualize AR, thetrajectory and its intercepts may be visualized as projected on avertical plane (AR plane) passing through the radar system and mortar,and to visualize AA, a similar projection may be made on a plane (AAplane) at right angles to the radar-mortar line. In each case, thetrajectory will be fore-shortened by the cosine of the angle between thetrajectory plane and the plane on which the projection is made. Themortar is located on the ground in polar coordinates to a firstapproximation as RH-KAR; A +KAA. The computer can thus determine themortar position by storing the information R and A calculating AR and AAfrom information set in by the operator, and performing the necessarymultiplications and additions to obtain the desired result.

The foregoing calculations have been based on a straight lineextrapolation and will result in quantities KAR and KAA which are toogreat and tend to overshoot the actual mortar position, due primarily tothe parabolic nature of the actual trajectory T. In other words, thecalculations approximately find point 1" instead of point M. Due to theassumption that the distance ac in FIGURE 2 is equal to the differencein range R R =AR (which assumption is not entirely true), the overshooterror arrived at by assuming a straight line extrapolation is somewhatreduced, at least as far as range is concerned. it is not reduced inazimuth since the assumption just mentioned forms no part of thegeometry of FIGURE 3. Indeed, at certain angles of sight and angles ofmortar fire, the point f (as calculated by using the multiplication KARas explained) can even lie between the mortar M and the radar system RDin FIGURE 2.

The distance M (or My) may be found in terms of the parameters of atypical parabolic trajectory with reference to FIGURE 5, Dx being thedirectrix of the parabola, and p being the semi-latus rectum.

For any parabola S =2ph.

Also V the velocity of the projectile in the x direction at point a, isequal to the distance travelled, x, divided by the time taken. Theprojectile is assumed to be subject to gravity only, and the horizontalcomponent of the velocity to be constant.

Thus:

When x=S and t=f which occurs at the vertex, from the combination of theforegoing equations y fi*p The vertical component V of the projectilevelocity at point a is given by the well known expression for aparabolic trajectory ya "'y) It now the equation S =2ph is expanded forany point on the parabola, it becomes x=' /2ph- /2ph2py with the signrepresenting an imaginary case.

The distance L shown in FIGURE 5 is given by the geometry of the systemfrom the relationshi Arc i KS

v Vya and using the above expression for x gives ar/2 i If we nowsubstitute in this equation the expressions for V and V we get x29 XEKY8 Now, in the AR plane,

where AT is the time between intercepts.

Also x=KAR, where K' is the corrected value of K to obtain the truemortar position.

Substituting, we get w y Vxa ya VII! Since the variables V and V will befound not at point a but at a point half-Way between a and b '(seeFIGURES 2 to 4) the quantity K should read The reason for this is that Kis the corrected value of K which latter should really be t a (iibi fora point mid-way between points a and b. This expression a5 a :K-I-Vz (orK'+ corected) It should be remembered that K and K are pure(dimensionless) numbers.

The equation to be solved becomes then ZaR RAA AT then rc g (KRAAWgWavy? w AT X AT gK AT R AA 2aR AA gK AT AA 241 Since this is actualdistance, and in this case We require an angular correction, the anglewill be gK AT ZaR AA the same as before.

This expression is also modified further to substitute K+ /2 for K tobecome so that we now have the same multiplier, K, for both AR and AA,as given by Examination of FIGURES 2 and 3 shows that someapproximations were made. For example in FIGURE 3 (AA plane) In FIGURE 2it is apparent that the greater part of the error is due to theapproximation 7 ca:R R =AR where the distance as is the actual AR andThe distance cu can be approximately ordinary trigonometry as cuzoz 0+3Rm Where Rm is the range from the radar system RD to the mortar 1 Thisequation is derived from the fact that the distance bs is given by thewell known expression 1 r bs=2R2 sin' Since the angle between the linebis and the line cb determined by V 9 is equal to then cuzba sin (0+3)@2122 sin; sin (0+3) Rma 0+ Taking a=40 mils, and Rm in meters, and 0 inmils, this equation becomes N (6+20)Rm Thus the true target (mortar)position in polar coordinates from the radar system RD, where Am is theangle between North and the line of sight to the target, are given byequations Rm sine Am and Rm cosine Am If the radar position is added tothese quantities as Eastings and Northings then Rm sine Am-l-RadarEastings: Target Eastings Rm cosine Am+Radar Northings=Target NorthingsBesides determining the target position in plan, the computer willprovide an elevation (in feet above sea level) of this position. vThisis necessary for the operator to determine the correct angle of theworking plane WP. The elevation of the target relative to the radar isRm sine 5 but for simplicity, and because q) is always small, this istaken as Rm With being measured downwards from the horizontal, theequation for elevation becomes Rm+Radar Elevation=Target Elevation Themanner of use of this information by the operator is described below.

Nature of echo presentation and operators procedure (FIGURES 6 and 7)Attention is now directed to FIGURES 6a, b and c. FEGURE 6a shows a planview of a typical sector scanned by the radar RD. Two composite echodisplays E and E produced by the lower and upper beams, respectively,are shown. FIGURE 6!) demonstrates the manner in which the sector SR ispresented on the screen lb S of a B-scope, that is to say a scope whichexhibits azimuth along the horizontal axis and range along the verticalaxis. After having detected a weapon firing, the operator will enlargethe critical area of the sweep as demonstrated by FIGURE 60.

The echo displays actually received in practice are more complex thanthose illustrated in FIGURES 6a, b and c, and attention is nowtransferred to FIGURES 7a to f for a more detailed discussion of thenature of the display on the screen actually observed by the operator.

As a projectile enters the field of scan of the lower beam, an echo E1is displayed on the screen S by a group of individual signal returnsresulting from a single passage of the narrow beam across theprojectile. The center of the leading (lower) edge of this echo (pointC1) represents the true position of the object (projectile) beingobserved. As the beam continues to sweep, a series of such echoesappears on the screen S. These echoes are indicated as E1 to E5 inFIGURE 7!; and make up the composite echo E of FIGURES 6a to c. Inreality there may be many more than five individual echoes in thisseries. Echoes E1 to E4 are shown in broken lines because some fadingwill have taken place by the time the last echo E5 appears. The duty ofthe operator is to observe or mark the centre points C1 and C5 of theleading edges of the first and last echoes and to estimate the meanpoint CML between these two eX- treme centre points. The screen S isprovided with an outer surface that can readily be marked by theoperator using a suitable stylus. He may mark points C1 and C5 on thescreen as echoes E1 and E5 appear, and then estimate and mark the meanpoint CML, but an experienced operator will be able to estimate quiteclosely the mean point CML and mark it on the screen merely byobservation of the series of echoes, without finding it necessary to gothrough the preliminary stage of actually marking points C1 and C5. Thevital point to obtain as accurately as possible for the purposes ofsubsequent operation of the computer is the mean point CML of thecentres of the leading edges of the series of echoes LR resulting fromthe lower beam.

Assuming that the mortar is firing from left to right and towards theradar system RD, the second series of echoes UR detected by the upperbeam and shown as composite echo E in FIGURES 6a to c appears first asan echo E6 (FIGURE and continues down to echo Eli (FIGURE 7d). Theseechoes of the second series will similarly have leading edge centrepoints C6 to C10, the mean point of which is designated CMU. The upperbeam echoes will appear in a lower position on the screen S than thelower beam echoes when the mortar is firing towards the radar, since therange will have shortened somewhat by the time the projectile reachesthe upper beam.

Thus, by the time all the echoes have faded from the screen S, theoperator will have marked at least the points CML and CMU, which pointsrepresent the mean positions of the projectile as it passed through thelower and upper beams respectively. It has been found in practice that.a skilled operator can assess the positions CML and CMU to anacceptable degree of accuracy even though estimating these pointsrequires visual and manual dexterity.

As well as carrying out the functions just described, the operator willtime the interval the projectile takes to pass from the lower to theupper beam. He can do this either by comparing the first echo of eachbeam, the last echo of each beam or any pair of corresponding points onthe two beams. It has been assumed in FIGURE 7 that he uses the firstmethod and records the time between the respective first echoes E1 andE6 of the lower and upper echo series LR and UR. For this purpose, theoperator has a hand switch HS situated beside the screen S. Arighthanded operator will push the switch HS with his left hand, toleave his right hand free for marking the screen S. A second, paralleloperating, hand switch HS is provided for left-handed operators. AsFIGURE 7a indicates by an arrow, the operator will push in the switch HSimmediately on appearance of the first echo E1 of the lower beam. Thisoperation will start the timer TM. When the first echo E6 of the upperbeam appears (FIGURE 70) the operator will again push the hand switch HSto stop timer TM which will now remain in its new position indicatingAT, the time of travel from the lower to the upper beam by theprojectile.

As FIGURE 7e demonstrates, the operator is left, after passage of aprojectile, with two points CML and CMU marked on his screen S, and ATrecorded in the timer TM.

The screen S is also provided with a marker spot MS, which is anelectronic marker produced by conventional circuitry in the radartransmitter-receiver combination and synchronised with the scope sweepso as to occupy a single desired position on the screen S determinedhorizontally by an azimuth marker handwheel AMH and vertically by arange marker handwheel RMH; Reference may be made to E. F. V. RobinsonCanadian Patent No. 580,247, issued July 28, 1959, for a description ofa system for achieving this result. The operator first moves the markerspot MS by means of the handwheels AMH and RMH to coincide with thepoint CML and when he has achieved this coincidence he presses a footswitch FS (FIGURE 7e). Depression of switch FS brings the computer intofull operation, as will appear in more detail below. Althoughillustrated simply, the switch FS is a toggle switch of the typecommonly employed to raise and lower the headlights of an automobile,that is to say a switch which remains in each acquired position untilreactivated by a further depression of the operators foot to bereversed. As demonstated by FIGURE 7], after closing switch PS theoperator moves the marker spot MS with handwheels AMH and RMH to thepoint CMU, while switch FS remains closed. In this way, the operatorfeeds into the computer the ditference in range AR and the difference inazimuth AA between these two points.

Operation of the computer (FIGURES 8 to 12) For an understanding of themanner in which the target point is calculated from the informationavailable, reference will now be made to FIGURES 8 to 12.

FIGURE 8 shows as a single block RDR a radar transmitter and receiverassembly with related circuits for the B-scope and the electronic markerspot MS. These circuits are conventional and their particular natureforms no part of the present invention. Assembly RDR iscoupledelectrically and mechanically to the antenna ANT comprising thescanner-reflector assembly already described.

The computer portion of the circuitry which the remainder of FIGURE 8illustrates in general layout can conveniently be roughly divided intoportions which deal respectively with range, elevation, azimuth andinformation display. These circuit portions are treated separately andin more detail in FIGURES 9, 10, 11 and 12. respectively. Although thesecircuits are interrelated sufficiently to require some reference to eachother in understanding, the description which follows will, as far aspossible, take eachcircuit separately and examine its composition andfunction. (In all these circuit diagrams, broken lines signifymechanical connection, full lines electrical connection.)

The range circuit portion (FIGURE 9) G1 controls the range position ofthe marker spot MS on the screen. It also, through shaft H4, operates acam CAM7 which controls a pulse repetition frequency switch PRFS. Thisswitch changes over the radar system from short to long range.

At the same time the handwheel motion is transmitted by shaft H1 to afirst input of a mechanical differential D1. Thus, when the marker spotMS is moved to the point CML in FIGURE 7a, the range R of such point isfed into the differential D1. As already explained, once the marker spotMS has been aligned with point CML, the operator operates foot switch FSwhich remains closed. As shown in FIGURE 9, foot switch FS serves toener gize a mechanical clutch CL2 which now connects the shaft H1 of thehandwheel RMH to shaft H3 which forms another input to differential D1acting in opposition to shaft H1. As a result, when the marker spot MSis moved by the operator towards point CMU (FIGURE 7 the output ofdifferential D1, shaft H2, remains stationary since AR (the rangedifference between points CML and CMU) is being inserted twice inopposite sense into differential D1. The position of shaft H2 representsthe range value R1, while shaft H3 is moved a distance equal to AR.

Foot switch FS energizes relay RY, one pair of contacts RY1 of which isopened to de-energize a clutch CL1 which had hitherto been holding shaftH3 under the control of a motor M1. Contacts RY2 which are closed byenergization of the relay RY serve to ground the input to a motor returnamplifier MR1 de-energizing motor M1. The zeroing function of this motorM1 will be described below in connection with the resetting of thesystem.

The factor -AR is transmitted by shaft H3 to a movable slider on aresistor RRZ. This part of the circuit is concerned with simulatingEquation 1 above, which for convenience is here repeated.

Rm=R K[AR+a el-g Rra] 1 If the last term is called I, this equationbecomes 7 Rm=R +K'(AR+J) (la) And if numerical values are inserted, thisequation becomes The factor I is added to AR by m is of resistors RRSand RR9 arranged in series with resistor RR2. Resistors RR8 and RR9 eachhave a movable slider controlled through a shaft H6 by a motorMZ whichis made to turn by an amount representing the factor J, as will now beexplained. By definition J is equal to the angle of sight 0 plus aconstant, multiplied by the range Rm, all divided by a further constant.The range Rm is inserted by a shaft H9 controlling a slider on aresistor RR5, and 0 (the angle of sight) is inserted by a shaft H18controlling a slider on a resistor RR6. The constant is added.

to 0 by choice ofthe initial position. Movement of shaft H10 iscontrolled by the elevation circuit portion shown in FIGURE 10 anddescribed below. A relay RZ shown in FIGURE 10 controls contacts R21 andRZZ to close the former and open the latter after hand switch HS'sentative of the product of the positions of the sliders on resistorsRRS and RR6, namely Rm(0+a constant). Servo-amplifier SAl energizesmotor M2 to-drive its shaft H6a to reorient the position of a groundedslider on a resistor RR7 in such a way as to restore the input to theamplifier SAl to zero. This servo-loop thus maintains the shaft H6 atall times at a position representative of the function I, the constantin the denominator of this 13 expression being provided by themechanical ratio between shafts Ho and Hea.

As noted above, shaft H6 is connected to the movable sliders onresistors RRti and RR9 whereby the combination of these resistors withresistor RRZ generates the function AR-I-J.

It is now necessary to form the product of such latter function and thefunction K. The function 4 is inserted into the system of FIGURE 9 atthe slider of a resistor RR3 by a shaft H7 the position of which iscontrolled in the manner subsequently described in connection withFIGURE 10. Resistor RR3 is series connected with the slider on resistorRR2 by contacts RY3 which are closed when relay RY is closed and theresulting product output is connected through closed relay contacts RYdto a servo-amplifier 8A2 which controls a motor M3 the shaft H8 of whichmoves a grounded slider on a resistor RR]. in a manner to restore theinput of amplifier SAZ to zero. These parts thus form a secondservo-loop whereby the shaft H8 is maintained at all times in an angularposition corresponding to the function K(AR+J).

A second differential D2 receives input from shafts H2 and H8 to formthe sum of R and K(AR}J), which sum is Rm in accordance with Equation1a). The function Rm appears at the output of differential D2, shaft H9,to be fed into target range counter GT1 which indicates the targetrange. Shaft H9 also moves sliders on resistors RRIl and RRl for reasonsthat will appear when FIG- URE 10 is considered, moves a slider on aresistor RRIti for a reason that will appear when FIGURE 12 isconsidered, transmits the Rm function to the slider of resistor RRS forgeneration of the I function in the manner already described, andoperates a cam CAM which actuates range change-over switches RG51 andRGSZ which change the computer over from short range to long range byaltering the supply point of power to resistor RRiti and its presetbalancing resistors RRltia and RRltib.

When foot switch FS is reversed to tie-energize relay RY, contacts RYlticlose to apply the return signal to servo-amplifier SAZ which causesmotor M3 to centre the slider on resistor RRl. Contacts RYl also closeto energize clutch GL1 to connect shaft H3 (clutch GL2 now beingdoe-energized) to motor M1 for return to zero position under the controlof motor return amplifier MR1 which is now connected through contactsRYH to the slider of resistor RRZ. The slider of this AR resistor RRZ isthus returned to centre position through the zeroing of shaft H3.Contacts RY4 cause motor M3 to return the slider of resistor RRI tocentre position. These two potentiometers will then remain in thisposition until a new problem is set in and the foot switch FS is againressed to close relay RY.

The elevation circuit portion (FIGURE 10) Turning now to FIGURE 10, theangle of sight 9 of the antenna ANT is fed to the computer from asynchrotransmitter ST geared to the antenna. This information concerningthe value of 6 is applied to the stator of a control transformer B3 anddevelopes an error voitage in its rotor, which voltage is applied as aninput signal to a servo-amplifier SA3 controlling a motor M4, the outputshaft H10 of which turns the rotor of control transformer B3 to cancelout the error voltage and thus complete the servo-loop. Shaft Hit) alsocontrols the slider on resistor RRe as already described in FIGURE 9,feeds to an angle of sight indicator I1, and is applied as an input to adifierential D3.

As already explained, the operator commences by estimating the workingplane WP from a contour map and by setting such estimate of the angle ona working plane handwheel WPH. The shaft Hltfi of haudwheel WPHtransmits motion to a working plane indicator 12, as well as to a secondinput of differential D3 and to the slider of resistor RRIS. The outputof differential D3 is a shaft H12 which thus represents the factor(9-[-q'2).

By adjustment of the gear ratio this factor can be divided by a constantto derive the factor K which equals The output of differential D4(representing K) is applied to shaft H7 which, as already indicated, isfed to the slider of resistor RR3 in FIGURE 9. It is also fed to theslider of a resistor RRZIl of the azimuth portion of the circuit to bedescribed in connection with FIGURE 11, and to the slider of a resistorRRItZ of a. circuit now to be described.

The factor Q applied to differential D4 by shaft H13 is derived inanother servo-loop formed as a bridge. The inputs are factor Rm atresistor RRll (from FIGURE 9), factor K at resistor RRiZ (which resistorby virtue of additional end turns is made to represent the function K+/2), and AT, the time function, at resistor RR13. (Derivation of factorAT will be explained below.) Servo-amplifier SAA- monitors the output ofthe bridge and controls a motor M5 to restore equilibrium by movement ofthe slider of a resistor RRM forming the fourth arm of the bridge. Theposition of motor M5 is also transmitted by shaft H13 to differentialD4. The resistors R1212 and RRI3 at which factors K t-V2 and AT areinserted are wound as square law otentiometers. Resistors RRH and RRMare linear. But appropriate ad justment of the constants, the factor Qis obtained at shaft Hi3 equal to (KW-$4) AT Servo-amplifier 8A4 is camcontrolled through contacts CCl from the AT circuit, so that thisservo-loop can only function when AT has been set into the computer.

The AT circuit (FIGURE 10) operates as follows. Motor M5 is acontinuously running synchronous motor and its shaft H14- can beconnected to shaft H15 controlling resistor RRElS and cams CAMl and CAMZby means of a clutch GL3. Clutch GL3 is energized through contacts M1 ofa latch relay RX controlled by hand switches HS and HS previouslydescribed in connection with FIGURE 7a. The relay RX is of a type whichlatches alternately in and out upon subsequent energizations. Upon beinglatched in by initial actuation of say switch HS as demonstrated inFIGURE 7a, contacts RXl are closed to energize clutch GL3 and transmitthe rotation of the motor M6 to shaft H15 thus beginning to count thefactor AT on timer TM. Indicating lamp LPZ is deenergized at this timeby opening of contacts RXZ.

As soon as shaft Hi5 starts to turn, cam GAME closes contacts GGl topermit the servo-loop of servo amplifier 8A4; to operate, and cam GAMZopens its contacts CGZ and closes its contacts (303. Assuming that handswitch BS or HS i again actuated by the operator before cams GAME andGAME; and timer TM have completed one full rotation (as in FIGURE 70),contacts GGL GGZ and GGE: remain in their new positions when, upon thesecond closing of switch H8 or HS, the relay RX is returned to itsinitial position to de-energize clutch GL3 and leave shaft H15 in theposition it has acquired representing the factor AT. With this ATinformation thus stored in shaft Hi5, as soon as the foot switch FS isclosed (FIGURE 7e) a circuit is completed through closed contacts GC3 toenergize a relay RZ which closes contacts R21 and opens contacts R22 inthe circuit generating the I function (see FIGURE 9). At the same timeindicating lamp made to FIGURE 11.

LPl is lit. In this way the J function can only be applied when the ATfactor has been set in and the foot switch FS is in the actuatedposition. However, if the projectile is known to be of the type having astraight line trajectory such as a self-propelled rocket, it is possibleto retain the I function while removing the Q factor from the equations.This effect is achieved by closing a rocket switch ROG which shortcircuits the active portion of resistor RR13. Th result is anapproximately straight line extrapolation, the most appropriate for thistype of projectile.

Another part of the circuit shown in FIGURE 10 is that derived from theshaft H11 of the working plane handwheel WPH to control the position ofa slider on a resistor RRIS. This part of the circuit is designed toderive the elevation, which is a function of the working plane angle andof the range Rm which is applied by movement of a slider on a resistorRR16 (FIGURE 9). This is another servo-loop consisting of aservo-amplifier 8A5 controlling motor M7, the output shaft H17 of whichadjusts resistor RR17 to restore the input of amplifier SA5 to zerowhile the output from shaft H17 is also fed to another differential D5.The known elevation of the radar system is applied at radar elevationhandwheel RLH and is fed by shaft H16 to appear directly in counter GT3while being added in differential D5 to the difference in elevationbetween the radar system and the target, Rmq5, as determined by thechosen working plane, to give the elevation of the target in shaft H5and counter GT4.

In operation, once the operator has a first reading of the target point,he checks to see if the elevation appearing in counter GT4 agrees withthe elevation shown on his map of the target location. If it does not,he turns the working plane handwheel WPH until the counter GT4 shows theelevation given by the map at the target location as determined by thecomputer. This adjustment is automatically applied to all the otherdependent variables in the system and a new location is immediatelycomputed. The operator then rechecks the map elevation and makes afurther adjustment if necessary (normally only one resetting isrequired).

The azimuth circuit portion (FIGURE 11) y We come now to considerationof the manner of determining azimuth, for which purpose reference shouldbe Information concerning the antenna azimuth AA is supplied to thecomputer by an assembly consisting of two synchro-transmitters 8T2 andSTE, one geared directly to antenna azimuth rotation and the other(Vernier) rotating 15 times per antenna rotation. This synchroinformation is applied to the stator of respective main and Verniercontrol transformers B4 and B5. Since these rotors are not free to turn,an error voltage is developed in one or both rotors if they are notaligned with the actual antenna position. These error voltages areapplied to a signal selector SS which receives inputs from the rotors ofboth the main and Vernier transformers B4 and B 5. As soon as the inputfrom the main control transformers B4 is above a specific voltage levelthen this error signal vcontrols the output of the signal selector SS.When the error signal from transformer B4 drops below this level, i.e.approaches a null, then any signal being developed by the verniercontrol transformer B5 becomes the controlling voltage and is passed bythe signal selector S5. The output of signal selector SS passes to aservo-amplifier 8A6, and theservo-loop is completed by a motor M8,the'shaft H18 of which is connected to the rotors of transformers B4 andB5. Motor M8 thus drives the control transformers to their correctnulls. Should the main control transformer B4 reach its wrong null, i.e.3,200 mils out, then the controlling voltage from the Vernier controltransformer B5 will drive the servo away from this null towards thecorrect one, so that the system will only stabilize itself on thecorrect azimuth setting.

Shaft H18 of motor M8 also drives through a differential D6 to appear onan antenna azimuth counter GT5 via shaft H19, which also transmits thismotion through a differential D7 to a shaft H20 and a target azimuthcounter GT6. An azimuth orient handwheel AOH controls a shaft H21 alsofeeding into differential D6. In setting up, this handwheel AOH isrotated until the antenna azimuth counter GT5 reads the correct bearingof the center of scan of the antenna to a known target. In this way theantenna azimuth is oriented in respect to a compas hearing such asNorth. Shaft H21 is then locked by lock HQ.

Shaft H19 also feeds into a further differential D8 which receives asecond input from the azimuth marker handwheel AMH via shaft H21. Theoutput of differential D8 is recorded in an antenna marker counter GT7.An azimuth potentiometer AZP controlled by shaft H21 controls theposition of the marker spot MS in azimuth on the screen S. In additionto driving differential D8 the azimuth marker handwheel AMH also drivesdifferential D9, a i marker counter GT8, and one side of a clutch GL4.

Differential D9 may be considered as a storage device. It functions soas to have an output which indicates the position of the marker spot MSat the first intercept point GML. When the marker spot MS is alignedwith point GML (FIGURE 70) the foot switch FS is closed to energizeclutch GL4 so that any further motion of the azimuth marker handwheelAMH is applied both directly to differential D9 by shaft H21, and inopposite sign to the same differential through clutch GL4 and shaft H22.Such applications thus subtract from one another. Differential D9effectively stores the azimuth position of the marker spot MS at thepoint GML, namely A and passes this information on through shaft H23 todifferential D10.

Shaft H22 which only starts to turn after foot switch FS closes clutchGL4 thus provides a measure of AA, the difference in azimuth, and thisfunction is transmitted to a slider on a resistor RR20 of a furtherservo-loop designed to provide the multiple KAA. The factor K isinserted at the slider of resistor RR21 being obtained from shaft H7 ofthe FIGURE 10 circuit. Resistor RRZl is series connected by contacts RY7of relay RY (when energised by foot switch FS) with the slider ofresistor RR20. The output which traverses now closed contacts RY8appears at the input of servo-amplifier SA7 to control the posit-ion ofmotor M9 which in turn controls the slider of a resistor RR22 throughshaft H25 in a manner to restore the circuit to balance.

The position of shaft H25 then represents the function K'AA which isapplied at differential D10 to be added to factor A and hencetransmitted through shaft H24 to be added in differential D7 to theantenna azimuth to provide an output in shaft H20 which representstarget azimuth, Am. See Equation 2, Am=A +KAA. This value Am appears intarget azimuth counter GT6 and is also fed to a resolver RS shown inmore detail in FIG- URE 12.

When foot switch FS is reversed to de-energise relay RY, contacts RY9close to apply the return signal to servo-amplifier SA7 which causesmotor M9 to centre the slider on resistor RRZZ. Contacts RYS also closeto energize clutch GL5 to connect shaft H22 (clutch GL4 now beingde-energized) to motor M10 for return to zero position under the controlof motor return amplifier MR2 whieh is now connected through contactsRY1-2 to the slider on resistor RR20. The slider of this AA resistorRR20 is thus returned to centre position through the of FIGURE 11 allowsthe centering of the radar scan on the position of these echoes. Theamount and direction of rotation of the antenna may be initiallydetermined by the azimuth marker spot setting or approximated by theoperator and set on centering dial CD through shaft H26 by azimuthcentering knob ACK. Clutch GL6 and the antenna relays are ale-energizedwhile knob ACK is being turned, but operate as soon as torque is removedfrom the centering knob. Shaft H26 also controls cams CAM-i and CAM4which respectively operate clockwise antenna rotation switch CWS andcounter-clockwise antenna rotation switch CCWS. These switches controlthe antenna ANT so that it will rotate automatically in the directionand the amount set on dial CD.

As a second embodiment of this azimuth centering device (notillustrated), the cams CAM3 and CAM4 are both attached to shaft H21instead of shaft H29. A suitable clutch arrangement is then providedcoupling the antenna azimuth shaft H18 to the shaft H21. A manual switchprovides excitation for this clutch arrangement as well as for switchesCWS and CCWS which remain mechanically actuated by cams CAMS and CAMd tocause the antenna to rotate automatically until the marker spotdisplacement is removed. This thus constitutes a fully automatic azimuthcentering device.

The information circuit portion (FIGURE 12) FIGURE 12 shows theinformation portion of the system which is provided to convert thetarget ranges and azimuths to Eastings and Northings. This isaccomplished by obtaining a voltage proportional to tar-get range Rmfrom resistor RRltl (see also FIGURE 9) and applying this voltage to thestator RSS of the resolver RS through a booster amplifier BA, while therotor RSR of the resolver RS is rotated in proportion to the targetazimuth Am obtained from the shaft H of FIGURE 11. The outputs of thewindings of the resolver rotor RSR are then proportional to Rm sine Amfor Eastings and Rm cosine Am for Northings, such Eastings and Northingsbeing the relative Eastings and Northings of the tar-get in relation tothe radar system. Amplifier AR3 and motor M12 form a servo-loop for theEastings with an output in shaft H which drives a slider on resistorRRStl until its voltage is exactly equal and opposite to that generatedin the rotor winding of resolver RS to which such slider is connected.Similarly, amplifier AR2 and motor M13 form a servo-loop for theNorthings giving an output in shaft H31 driving the slider of resistorRR-31. Resistors RR30 and RR3 1 are supplied with power from points W,X, Y and Z as indicated from FIGURE 9. A differential D12 driven byshaft H30 has the known radar Eastings applied to it by radar Eastingshandwheel REH and shaft H32. A differential D13 driven by shaft H31 hasthe known radar Northings applied to it by radar No-rthings handwheelRNH and shaft H34. Absolute radar Eastings appears in counter GT9, whilethe sum of shafts H30 and H32 appears in shaft H33 as the targetEastings (that is the absolute target Eastings) and is displayed incounter CF10. In a similar manner, absolute radar Northings appears incounter CTll, while the sum of shafts H31 and H34 appears in shaft H35as the target Northings (that is absolute target Northings) and isdisplayed in counter CT12. Shafts H32 and H34 are normally clamped bylocks LKZ and LK3.

Reconsideration of overall system Returning to a consideration of FIGURE8 in the light of the details of FIGURES 9 to 12, it will be observedthat each of these figures has been shown as a single block in FIGURE 8,although certain of their parts such as handwheels, counters and shaftshave been shown separately for emphasis. FIGURE 8 is intended toillustrate concisely the interrelationship of the circuits of FIGURES 9to 12, and to show the principal functions that are exchangedmechanically and electrically between these circuits. i

l O I a The inputs to the computer supplied by the operator are AME-theazimuth marker handwheel,

RMH-the range marker handwheel,

WPH-the working plane handwheel,

RLHthe radar elevation handwheel,

REH-the radar Eastings handwheel,

RNI-Ithe radar Nor-things handwheel,

AOH-the azimuth orient hand-wheel, and

AT-the time interval between observing the projectile V in a likeposition in the lower and upper beams.

The information obtained from the antenna comprises 0the angle of sight,and AA-the antenna azimuth.

The principal outputs are in CT-the target elevation counter,

CT6--the tar-get azimuth counter, CT1the target range counter, CTltl-thetar-get Eastings counter, CTiZ-the target Northings counter.

If it is desired to determine any target point on the trajectory otherthan its point of intersection with the ground, the operator may inclinethe working plane until the required height appears in target elevationcounter GT4. This facility is particularly valuable in directingfriendly lire when the shells are fused for air burst.

Resetting procedure (FIGURES 9 to 11) After making an observation andcomputation as above described, the operator resets the computer bydepressing the foot switch F8 for a second time to open its contacts andde-energize relays RY and RZ. The K'AA and K'(AR+J) shafts H25 and H3are returned to zero by motors M9 and M3 as described and the AR and AAsha fts H3 and H22 are also returned to zero by motors M1 and M10. Theoperator again presses his hand switch HS (or HS) to re-energize relayRX and reen- -gage clutch 0L3 so that shaft H 15 again starts to turn.Such motion continues until cams CAMl and CAMZ and timer TM eachcomplete one full revolution. Resistor RR13 similarly completes oneexcursion (revolution) to return to its zero position. Cam CAM-1 openscontacts CC-ll which causes servo-amplifier SA E- to operate motor M5 toreturn the slider of resistor RR14 to zero and then becometie-energized. Cam CAM2 opens contacts CO3 and closes contacts CO2.Closing of contacts CO2 completes a circuit through contacts RX3 ofrelay RX to re pulse this relay to return it to and latch it in theposition in which contacts RXl and RX3 are open. This opens clutch 0L3to stop shaft H15 with the cams in their zero positions. Now closedcontacts CC?) and RX2 relight lamp LP2 to indicate that resetting hasoccurred.

The system is now in readiness for a new set of values to be fed into itwhen the operator observes another projectile in flight.

Calculation of muzzle velocity and time of flight (FIGURES 13 and .14)

The enemy weapon is again assumed in FIGURE 13 to be a mortar M tiring aprojectile in a trajectory T. Such trajectory T is observed by the twobeams P1, P2 of the radar system RD, in the manner explained above. Atintercept point a, assumed to be the centre of the lower beam P2, theprojectile has a vertical component of velocity V At point b, thisvertical component is V The average of V and V is V Now with AT the a

1. A RADAR SYSTEM COMPRISING (A) MEANS FOR EMITTING TWO CLOSELYVERTICALLY SUPERPOSED, MUTUALLY DIVERGENT, GENERALLY HORIZONTAL,EFFECTIVELY CONTINUOUS UPPER AND LOWER RADAR BEAMS, (B) MEANS FORDISPLAYNG ECHOES RETURNED BY A PROJECTILE TRAVELLING IN A TRAJECTORYINTERSECTING SAID UPPER AND LOWER BEAMS AND FOR DETERMINING THE RANGEVALUE (R1) OF ONE OF SAID INTERSECTIONS MEASURED FROM THE RADAR SYSTEM,(C) MEANS FOR DETERMINING THE TIME INTERVAL ($T) BETWEEN PASSAGE OF THEPROJECTILE THROUGH CORRESPONDING POINTS OF THE UPPER AND LOWER BEAMS,(D) AND MECHANISM FOR SOLVING THE EQUATION